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Handling uncertainty in the case of lateral extension of log-porosity values in a turbidity reservoir

geological uncertainty can be determined through the differences between many equally probable reservoir descriptions generated using a geostatistical techniques known as stochastic simulations. Each of these realizations reproduces a prior measure of spatial continuity (covariances) and may be conditioned to honor available data. The differences between these descriptions provide indications of reservoir uncertainty due to lack of information (DEUTSCH, 2002). Sequential indicator simulation (SIS) is widely used for diagenetically controlled facies (DEUTSCH, 2002). However, the background indicator formalism can also be applied whenever the data set available has a considerable uncertainty (DEUTSCH & JOURNEL, 1997 ; JOURNEL & ALABERT, 1988). In case of Klostar field the number and spatial distribution of wells allowed us expecting any lateral extension of well-log porosity to be quite uncertain (NOVAK ZELENIKA et al., 2010). Because of this prior expectation we used the indicator formalism for discretizing the original well-averaged porosity data. Applying sequential indicator simulation for six porosity cut-offs we generated one-hundred equally probable stochastic realizations for each of five different grid sizes (Fig.1). Then the average values, the width of their probability intervals (Fig.2) and standard deviations were calculated for the first, first two, first three, and finally for the first 100 grids. The series of means obviously converged to the theoretical expected value of the background population. However the limit of series formed from the width of probability intervals did not equal zero. It means that even in the limit there is a small amount of uncertainty belonging to the information gathered about the porosity. It is an open question whether this uncertainty varies with the depositional genetic, but we demonstrated that it is the function of the grid resolution. To this there were generated 100 realizations (by repeating SIS procedure with the same parameters) for each of four different grid sizes. From these realizations we defined one hundred sets of realizations containing the first three, first four etc., first one-hundred realizations. For each sets the (1) average value, (2) the total variance, the (3) coefficient of variation and the (4) variation of the expected value were calculated. Afterwards, we decomposed the total variance into its (5) ‘inner’ (mean of the variances of at grid points) and (6) ‘outer’ (variance of the means among grid points) component for each sets of realizations. It has become clear, that according to the limit values and the speed of convergence the stochastic estimations (SIS) can be subdivided into two groups (Fig.3). These groups demonstrate where the change of scale can be made probable. Moreover this finding may reflect the scale of the representative elementary volume in the case of well-log porosity. It is also apparent that different numbers of realizations need for stabilizing the overall estimations when support changes.

formalism; Sequential Indicator Simulation; convergence; reservoir characterization; clastics; Miocene; Croatia

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